Bounding box as mesh?
One way to do it if your bounding box fits the object's dimensions:

1.) Select the Mesh Cube and then add the other object to the selection

2.) Copy the Dimensions and rotation info to the Cube

3.) Add Child Of constraint to Cube and select the object as the parent

4.) It will go wonky, so press the Set Inverse button in the constraint

5.) Finally, Restrict Selection so that it can't accidentally be manipulated